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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21137 |
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| _version_ | 1866914432205979648 |
|---|---|
| author | Yang, Yuxuan |
| author_facet | Yang, Yuxuan |
| contents | Given a number field $F$ and $R$ be the ring of integers of $F$, the problem of embedding a field extension $K/F$ into a central simple algebra $B$ is classical. This paper proves that when the central simple algebra has degree $p$, the $R$-order $S\subset K$ can be optimal embedded into all maximal $R$-orders $O\subset B$, unless satisfies the optimal selectivity condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal orders optimal embedding of central simple algebras over number fields Yang, Yuxuan Number Theory Rings and Algebras Given a number field $F$ and $R$ be the ring of integers of $F$, the problem of embedding a field extension $K/F$ into a central simple algebra $B$ is classical. This paper proves that when the central simple algebra has degree $p$, the $R$-order $S\subset K$ can be optimal embedded into all maximal $R$-orders $O\subset B$, unless satisfies the optimal selectivity condition. |
| title | Maximal orders optimal embedding of central simple algebras over number fields |
| topic | Number Theory Rings and Algebras |
| url | https://arxiv.org/abs/2511.21137 |